If your arm gets sore and tired, then that's probably a sign you need to be taking a break. You can always come back to the task later, or the next day, when your arm is feeling better and you're better able to draw using your whole arm, from the shoulder. Given that drawing with your whole arm engages muscles that otherwise are often unused, it's going to take some time and mileage to strengthen them, and increase your stamina. But no, the answer is not to slip back to drawing from your elbow.

Try giving these notes about the "path of least resistance" a read.